Has anyone tried to buid some sort of natural pool. Or should I call it a pond?

I don't want to use chlorine and don't want to refresh the water every now and then. Birds, frogs, fish and insects are welcome. On the other hand, I don't want to exit the pool covered in mud.

How big should it be to achieve a good balance?

I would caution against a fresh water pond. Mozzies breed on still (i.e. stagnant) fresh water.

Luckily, fish love to eat their larvae.